INF 223, Spring 2008, Plan of Lectures

This semester I will rearrange the course towards applications in (object-oriented) modeling and Model Driven Architecture. In the first part I will give an introduction into Category Theory based on Part 1 of the following book of Jose Fiadeiro Categories for Software Engineering In the second, applied part I will discuss the formalization of (diagrammatic) specification techniques like UML class diagrams, ER diagrams, database schemata, XML, ... I plan to close the course with an outline of a theory of model transformations based on this formalization. Articles and/or handouts, covering the second part will be made available during the course.

Nr. | Date | Week | Topics | Pages | |

1. | 21.01.08 | 4 | - What is Category Theory? - outline of the course | VII - XII, 1 - 11 | |

2. | 23.01.08 | 4 | - graphs and graph homomorphisms with examples - opposite graphs | 15 - 20 | |

| 28.01.08 | 5 | no lecture (cordination problems) | 20 - 22 | |

3. | 30.01.08 | 5 | - path in a graph - definition of a category with examples: SET, GRAPH - category of paths of a graph | 20 - 22 | |

4. | 04.02.08 | 6 | - category LOGI and general pre-orders as categories - category MULT of sets and multi-functions - diagrams and commutative diagrams | 23 - 27 | |

5. | 06.02.08 | 6 | - isomorphisms with examples: SET, GRAPH, LOGI - isomorphic objects have the same "social life" - monomorphisms | 27 - 29 | |

6. | 11.02.08 | 7 | - epimorphisms - split monomorphisms and split epimorphisms - opposite category - duality principle - subcategories, full subcategories and discrete categories | 29 - 32 | |

7. | 13.02.08 | 7 | - discussion of "typing" - slice categories - initial objects with example in SET | 33 - 38, 58 | |

8. | 18.02.08 | 8 | - initial and terminal objects - examples in SET, LOGI, MULT - definition of sum with example in SET, LOGI and for power sets | 58 - 65 | |

9. | 20.02.08 | 8 | - sums in slice categories - definition of product with example in SET, LOGI and for inheritance - definition of pushouts and pushouts in SET - equivalence relations and quotient sets | 65 - 70 | |

10. | 25.02.08 | 9 | - pushouts in SET - pushouts by sums and co-equalizers - actualization/instantiation as pushout | 70 - 75 | |

11. | 27.02.08 | 9 | - equalizers and pullbacks - general construction and examples of pullbacks - specializations of pullback and pushout constructions | ||

12. | 03.03.08 | 10 | - co-cones and colimits - cones and limits - completeness and co-completeness | 75 - 81 | |

13. | 05.03.08 | 10 | - stepwise construction of limits and colimits - diagrams as functors - functors with examples - category CAT | ||

14. | 10.03.08 | 11 | - examples and definition of free functors | ||

15. | 12.03.08 | 11 | - natural transformations - adjoint functors | ||

17.03.08 | 12 | no lecture (conference) | |||

19.03.08 | 12 | no lecture (conference) | |||

24.03.08 | 13 | Easter Monday | |||

27.03.08 | 13 | no lecture (conference) | |||

31.03.08 | 14 | no lecture (conference) | |||

02.04.08 | 14 | no lecture (conference) | |||

16. | 07.04.08 | 15 | |||

17. | 09.04.08 | 15 | |||

18. | 14.04.08 | 16 | |||

19. | 16.04.08 | 16 | |||

20. | 21.04.08 | 17 | |||

21. | 23.04.08 | 17 | |||

22. | 28.04.08 | 18 | |||

23. | 30.04.08 | 18 | - course overview | ||

05.05.08 | 19 | no more lectures |
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22/23 | Oral Exam | ||||